Lens stabilization comes in a variety of forms which differs from manufacturer to manufacturer (although sometimes not so much, as in the case of Sigma getting successfully sued for $14.5m dollars for infringing upon Nikon's patented design). Fundamentally it is a system inbuilt into modern optics or alternatively into some camera sensors, which helps to counter blur generated by camera shake. The shaking is caused by unsteady hand holding or shooting from a moving vehicle.
Although a prominent feature in a great deal of modern lenses, the technology itself is actually pretty old. Two decades old in fact, with image stabilization being first introduced in 1994 inside a compact camera called the Nikon Zoom 700VR. The technology was later adapted for DSLR lenses.
It works by a micro-computer calculating necessary adjustment to internal optics to counter the effects of detected movements via sensors in the lens. In Nikon's case, the Vibration Reduction starts with data gathered by two angular velocity sensors. One detects vertical movement, the other senses horizontal changes. Any diagonal movements are calculated by the combination of the results from both. All the while the VR is in effect (you half depress the shutter release button), the sensors perform their task 1000 times a second, with corrections being made to the internal elements instantaneously via two Voice Coil Motors or VCMs for short. Clever stuff, huh? It gets even cleverer though. The sensors can differentiate between shake and intentional movement. For example, if you focus and recompose, the micro computer can distinguish the differences.
There are now up to 3 different types of VR modes on certain Nikon lenses. What type(s) are featured depends upon the lens. On the Micro-Nikkor 105mm f/2.8 VR, there is only "Normal VR", which can either be on or off. Next is Normal or Active, which can be found on the 70-200mm f/2.8 VR II. This is when the photographer can select between the two. Active would be chosen if shooting from a moving vehicle such as a car or boat, or if you were walking whilst photographing your subject. Finally there is Normal/Tripod which by the name is pretty self explanatory. This feature is found on super-telephoto lenses in the 200mm to 600mm range (automatically on some, so there is no button for it).
Below is a list of stabilization abbreviations specific to each manufacturer. Note Sony and Pentax aren't mentioned because they opted for stabilization to occur on the image sensor, as did Olympus and Panasonic. .
Nikon Vibration Reduction - VR & VR II (3 and 4 stop improvement)
Canon Image Stabilization - IS & IS II
Sigma Optical Stabilization - OS
Tamron Vibration Control - VC
There is some misconception by newcomers to photography, that stabilization technology counters all blur types. Unfortunately, it doesn't. The only movement it can correct for is that which is introduced by the holder or external forces upon the camera. It has no effect on blur generated by movement of your subject matter. Only a fast shutter speed or strobe/speedlite can do that.
In low light conditions, often even shooting with the a wide aperture and high ISO isn't enough to achieve the shutter speeds required to avoid hand held blur. Absent a tripod, stabilization can make a huge difference in getting a sharp shot. Likewise when shooting from a vehicle.
Conversely, blur can actually be introduced if you are tripod mounted and have the "normal" image stabilization engaged. Always select the correct mode appropriate to the situation. You also need to ensure that when you do need it, that it is engaged and tracking, which may take a moment to do. If you fire off a shot with the VR enabled but don't give it time to track the movements, then again this can ruin your resulting image. It can take a little getting used to but, after a while you'll know how to use it properly.